Quiz 1_solution

Quiz 1_solution - 414 . 3 8 / 011287635 . 225 . 3 238625 ....

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IEN 312 Feb. 15, 2011 Quiz 1 Name: Eight independent measurements are taken of the diameter of a piston. The measurements (in inches) are: 3.236, 3.223, 3.242, 3.244, 3.228, 3.253, 3.253, 3.230 The sample mean is 3.238625 and the sample standard deviation is 0.011287635. Assume that these measurements come from a normal distribution with an unknown population mean μ . (a) Construct a 95% confidence interval for by using a Student T statistic . + - n s t x n s t x 7 , 025 . 0 7 , 025 . 0 , + - 8 011287635 . 0 2.365 238625 . 3 , 8 011287635 . 0 2.365 238625 . 3 [ ] 8 3.229,3.24 (b) Test the hypothesis 225 . 3 : 0 = H versus 225 . 3 : 1 H at a 05 . 0 = α significance level. Use the Student’s T statistic n s X T / - = with the critical region ( 29 ( 29 - , 365 . 2 365 . 2 , . Compute the t value under the null hypothesis:
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Unformatted text preview: 414 . 3 8 / 011287635 . 225 . 3 238625 . 3 / =-=-= n s x t Because 365 . 2 414 . 3 = t , we reject the null hypothesis and conclude that actual population mean differs from 3.225. (c) State the relationship between confidence interval and hypothesis testing by referring to your answers to (a) and (b). Testing hypothesis 225 . 3 : = H versus 225 . 3 : 1 H at 05 . = level is equivalent to computing a % 95 confidence interval on . If 3.225 is outside the confidence interval, we will reject the null hypothesis; on the other hand, if 3.225 is within the confidence interval, we will not reject the null hypothesis....
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